Does the Amazon Appstore work outside of the US?

Yes and No. No, it does not function as expected outside of the U.S.

This is because Amazon's One-click payment method requires a credit card issued by a bank in the U.S. and that has a U.S. billing address.

Therefore, the only way a customer in Canada could use the appstore is to meet this requirement. Amazon hopes to change this in the future and open it up to more international customers.